ABC storytelling is the art of telling a story (or sometimes a poem) using each of the manual letters of alphabet in order but maintains ASL structure (e.g. grammar).
An Ameslan or ASLian storyteller tells a story based on the handshapes of ASL signs from the handshape A to Z in the alphabetical order. For example, "A" for knocking on the door (which is very common), "B" for opening the door, "C" for shaking hands and so on.
The narrator can use various sequences, such as from A to Z, from Z to A, from AA to ZZ, or reversal. Although, the almost universal format is from A to Z.
While there are countless ABC stories, here is a few examples.
The video presents an ABC story, "The Great Horned Owl" by Erica Tara Lily Parker.
Because ASL is a language of its own (that is, it's not English!), a few alphabetical letters are problematic, specifically the alphabetical letter E which is not found in many ASL signs with the marked E handshape. If you ask why, then let's talk a bit in linguistics. A few handshapes found in the American alphabet are marked, that are less commonly used than unmarked handshapes.
For some alphabetical letters, the narrator often bend the rule of the pronunciation (production). For example, the handshape based on the manual letter A is not commonly found in ASL words, but the handshape A (loose thumb) is one of the most natural handshapes. So, the narrator will use that handshape for the alphatical letter A. Likewise for the handshape "B" (with loose or open thumb) for the letter B. And, so on. The bottom is that the handshapes of the alphabetical letters in ABC storytellng are a bit lenient.
If you are a native/fluent signer or an ASL student above level 200, try to make one of your own for fun. You don't have to go all the way from A to Z. You can do the first few or several alphabetical letters until your confidence runs out.